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  1. Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications (DIALM '01)
  2. L(2,1)-labeling of planar graphs
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Discrete models and algorithms for the capacitated location problems arising in UMTS network planning
Channel access scheduling in Ad Hoc networks with unidirectional links
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
L(2,1)-labeling of planar graphs
Selecting forwarding neighbors in wireless Ad Hoc networks
Oblivious gossiping in ad-hoc radio networks
A polynomial-time approximation scheme for base station positioning in UMTS networks
Reactive GRASP with path relinking for channel assignment in mobile phone networks
A mixed-integer programming model for the cellular telecommunication network design
On finding optimal registrations in presence of overlapping registration areas
An efficient approach for distributed channel allocation in cellular mobile networks

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L(2,1)-labeling of planar graphs

Content Provider ACM Digital Library
Author Petreschi, Rossella Calamoneri, Tiziana
Abstract In this paper we prove a conjecture left open by Bodlaender et al. [3] concerning L(2, 1)-labeling of outerplanar graphs. L(2, 1)-labeling is a coloring problem arising from frequency assignment in multihop radio networks, in which adjacent nodes must receive colors that are at least two apart while nodes at distance two must receive different colors. Namely, we improve the best known upper bound from Δ + 9 to Δ + 3 colors, Δ being the maximum degree of the graph and Δ ⪈ 8. Consequently, we improve the additive term for triangulated outerplanar graphs from Δ + 7 to Δ + 2, and for planar graphs from 3Δ + 29 to 3Δ + 8. We also make a step towards the improvement of the factor 3 in the bound of planar graphs; in fact we prove that for hamiltonian planar graphs 2Δ + 6 colors are sufficient.
Starting Page 28
Ending Page 33
Page Count 6
File Format PDF
ISBN 1581134215
DOI 10.1145/381448.381452
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2001-07-21
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Multi-hop radio networks Outerplanar graphs l(2 1)-labeling Planar graphs
Content Type Text
Resource Type Article
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